---
_id: '7683'
abstract:
- lang: eng
  text: For any free oriented Borel–Moore homology theory A, we construct an associative
    product on the A-theory of the stack of Higgs torsion sheaves over a projective
    curve C. We show that the resulting algebra AHa0C admits a natural shuffle presentation,
    and prove it is faithful when A is replaced with usual Borel–Moore homology groups.
    We also introduce moduli spaces of stable triples, heavily inspired by Nakajima
    quiver varieties, whose A-theory admits an AHa0C-action. These triples can be
    interpreted as certain sheaves on PC(ωC⊕OC). In particular, we obtain an action
    of AHa0C on the cohomology of Hilbert schemes of points on T∗C.
article_number: '30'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Sasha
  full_name: Minets, Sasha
  id: 3E7C5304-F248-11E8-B48F-1D18A9856A87
  last_name: Minets
  orcid: 0000-0003-3883-1806
citation:
  ama: Minets S. Cohomological Hall algebras for Higgs torsion sheaves, moduli of
    triples and sheaves on surfaces. <i>Selecta Mathematica, New Series</i>. 2020;26(2).
    doi:<a href="https://doi.org/10.1007/s00029-020-00553-x">10.1007/s00029-020-00553-x</a>
  apa: Minets, S. (2020). Cohomological Hall algebras for Higgs torsion sheaves, moduli
    of triples and sheaves on surfaces. <i>Selecta Mathematica, New Series</i>. Springer
    Nature. <a href="https://doi.org/10.1007/s00029-020-00553-x">https://doi.org/10.1007/s00029-020-00553-x</a>
  chicago: Minets, Sasha. “Cohomological Hall Algebras for Higgs Torsion Sheaves,
    Moduli of Triples and Sheaves on Surfaces.” <i>Selecta Mathematica, New Series</i>.
    Springer Nature, 2020. <a href="https://doi.org/10.1007/s00029-020-00553-x">https://doi.org/10.1007/s00029-020-00553-x</a>.
  ieee: S. Minets, “Cohomological Hall algebras for Higgs torsion sheaves, moduli
    of triples and sheaves on surfaces,” <i>Selecta Mathematica, New Series</i>, vol.
    26, no. 2. Springer Nature, 2020.
  ista: Minets S. 2020. Cohomological Hall algebras for Higgs torsion sheaves, moduli
    of triples and sheaves on surfaces. Selecta Mathematica, New Series. 26(2), 30.
  mla: Minets, Sasha. “Cohomological Hall Algebras for Higgs Torsion Sheaves, Moduli
    of Triples and Sheaves on Surfaces.” <i>Selecta Mathematica, New Series</i>, vol.
    26, no. 2, 30, Springer Nature, 2020, doi:<a href="https://doi.org/10.1007/s00029-020-00553-x">10.1007/s00029-020-00553-x</a>.
  short: S. Minets, Selecta Mathematica, New Series 26 (2020).
date_created: 2020-04-26T22:00:44Z
date_published: 2020-04-15T00:00:00Z
date_updated: 2023-08-21T06:14:58Z
day: '15'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1007/s00029-020-00553-x
external_id:
  arxiv:
  - '1801.01429'
  isi:
  - '000526036400001'
file:
- access_level: open_access
  checksum: 2368c4662629b4759295eb365323b2ad
  content_type: application/pdf
  creator: dernst
  date_created: 2020-04-28T10:57:58Z
  date_updated: 2020-07-14T12:48:02Z
  file_id: '7690'
  file_name: 2020_SelectaMathematica_Minets.pdf
  file_size: 792469
  relation: main_file
file_date_updated: 2020-07-14T12:48:02Z
has_accepted_license: '1'
intvolume: '        26'
isi: 1
issue: '2'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
publication: Selecta Mathematica, New Series
publication_identifier:
  eissn:
  - '14209020'
  issn:
  - '10221824'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and
  sheaves on surfaces
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 26
year: '2020'
...